Quantum mechanical machine vision system and arithmetic operation method based on quantum dot

ABSTRACT

A quantum mechanical arithmetic operation method for machine vision, based on quantum dots is performed by a quantum processing processor. The quantum mechanical arithmetic operation method comprises, obtaining a first labeled graph connecting between feature points of the first image and a second labeled graph connecting feature points of the second image, generating a point-to-point combination by matching the feature points of the first image with the feature points the second image, generating a conflict graph by adding the largest point-to-point combination by comparing the point-to-point combinations with the threshold, generating non-constrained binary optimization equation for finding a maximum independent set of conflict graphs, converting the non-constrained binary optimization equation into Ising model of the quantum system, and calculating the Hamiltonian of Ising model based on the quantum dots to obtain solution of the non-constrained binary optimization equation.

CROSS REFERENCE TO RELATED APPLICATION

This application claims priority from and the benefit of Korean PatentApplications No. 10-2016-0168244, filed on Dec. 12, 2016, which ishereby incorporated by reference for all purposes as if fully set forthherein.

BACKGROUND OF THE INVENTION Field of the Invention

The present invention relates to a quantum mechanical machine visionsystem and an arithmetic operation method, more specifically to aquantum mechanical machine vision system and an arithmetic operationmethod based on quantum dot.

Discussion of the Background

Human beings now have better analytical capabilities than machineanalysis in many areas such as object recognition, knowledgerepresentation, reasoning, learning and natural language processing.Accordingly, in order to imitate or surpass the human way of thinkingmechanically, a complicated arithmetic operation method must be used.

An accurate solution to the problem of optimization of machine visionsystem is required to imitate or surpass human visual recognitionability as an example.

In order to solve the complex computation method of artificial view,there is a method of performing quantum mechanical calculation usingquantum computing.

A quantum computer is a physical system that uses one or more quantumeffects to perform calculations. A quantum computer capable ofefficiently simulating other quantum computers is called a universalquantum computer (UQC).

1. Approach to Quantum Computation

There are several general approaches to the design and operation ofquantum computers.

One approach corresponds to a ‘circuit model’ of quantum computation. Inthis approach, qubits operate in the order of a logical gate, which is arepresentation of a compiled algorithm. Circuit model quantum computershave some serious barriers in their actual implementation. In a circuitmodel, qubits are required to be coherent for a longer period of timethan a single-gate time. This demand arises because circuit modelquantum computers require operations, called quantum error correction,to operate. Quantum error correction cannot be performed without thequbit of a circuit model quantum computer that can maintain quantumcoherence for a time interval of about 1000 times one gate time. Therehave been a number of studies focused on developing qubits withsufficient coherence to form basic information units of quantumcomputers. This is described in, for example, “Introduction to QuantumAlgorithms”, by Shor, P. W. arXiv. org: quantph/0005003 (2001), pp.1-27. This technical field is still stagnant due to the lack of theability to enhance the coherence of the qubit to a level suitable fordesigning and operating real circuit model quantum computers.

2. Computational Complexity Theory

In computer science, computational complexity theory is a kind ofcomputational theory required to solve a given computational problem andthe theory of computation to study resources or costs. Costs aregenerally measured by abstract parameters called computationalresources, such as time and space. The time means the number of stepsnecessary to solve the problem, and the space means the required amountof information storage or the amount of memory required.

Optimization problems correspond to problems where one or more objectivefunctions are minimized and maximized under a set of constraints,sometimes with respect to a set of variables.

Simulation problems typically deal with the simulation of one system byanother system during a typical time interval. For example, computersimulations consist of business processes, ecological habitats, proteinfolding, molecular ground states, and quantum systems. These problemsoften involve numerous diverse entities that are different from complexinterrelationships and behavioral rules. Feynman suggests that a quantumsystem can be used to simulate several physical systems more efficientlythan UTM.

Many optimization and simulation problems cannot be solved using UTM.Because of these limitations, computational elements are needed that cansolve computational problems beyond the scope of the UTM. Other digitalcomputer based systems and methods for solving optimization problems canbe found.

An example of a technique for solving this optimization problem isdescribed in Korean Patent No. 10-1309677 entitled ‘Method forCalculating Adoptive Quantum’.

The prior art discloses a quantum computing method using a quantumsystem that includes a plurality of qubits. In the prior art, quantumannealing is possible to obtain a desired minimum energy (or cost),which concurrently tracks a configuration of a superposition state, andespecially, Adiabatic Quantum Computation (AQC) technique is used toperform quantum annealing. In addition, AQC uses a technique in which anadiabatic change of Hamiltonian from the initial state to the targetstate is obtained and a solution of the desired target state is finallyobtained.

The above prior art describes the general operation of a quantumcomputing system to solve a complex problem, and in spite of theexistence of this prior art, the selection of an optimized quantumsystem remains a very important problem to solve the complicated matter.

SUMMARY OF THE INVENTION

Accordingly, it is an object of the present invention to provide aquantum mechanical machine vision system and an arithmetic operationmethod based on quantum dot, which can facilitate calculation ofcomplexity caused by an increase in the number of feature points forimage identification.

A quantum mechanical arithmetic operation method based on quantum dotsaccording to an exemplary embodiment of the present invention isperformed by a quantum processing processor. The quantum mechanicalarithmetic operation method comprises, obtaining a first labeled graphconnecting between feature points of the first image and a secondlabeled graph connecting feature points of the second image, generatinga point-to-point combination by matching the feature points of the firstimage with the feature points the second image, generating a conflictgraph by adding the largest point-to-point combination by comparing thepoint-to-point combinations with the threshold, generatingnon-constrained binary optimization equation for finding a maximumindependent set of conflict graphs, converting the non-constrainedbinary optimization equation into Ising model of the quantum system, andcalculating the Hamiltonian of Ising model based on the quantum dots toobtain solution of the non-constrained binary optimization equation.

For example, calculating the Hamiltonian of Ising model based on thequantum dots to obtain solution of the non-constrained binaryoptimization equation may be performed by quantum dots arranged in amatrix shape.

In this case, neighboring quantum dots with the shortest distance in acolumn direction or a row direction may be connected to each otherthrough the tunnel junction.

For example, the Hamiltonian of the Ising model may be calculatedthrough adiabatic evolve, in calculating the Hamiltonian of Ising modelbased on the quantum dots to obtain solution of the non-constrainedbinary optimization equation.

On the other hand, the quantum mechanical arithmetic operation methodmay further comprise repeatedly learning the non-constrained binaryoptimization equation through machine learning.

A quantum mechanical machine vision system according to an exemplaryembodiment of the present invention comprises an image acquisitionmodule, a quantum processing processor and a memory unit. The imageacquisition module acquires an image. The quantum processing processorprocesses the image obtained from the image acquisition module. Thememory unit stores data necessary for computation of the quantumprocessing processor. The quantum processing processor obtains a firstlabeled graph connecting between feature points of the first image and asecond labeled graph connecting feature points of the second image,generates a point-to-point combination by matching the feature points ofthe first image with the feature points the second image, generates aconflict graph by adding the largest point-to-point combination bycomparing the point-to-point combinations with the threshold, generatesnon-constrained binary optimization equation for finding a maximumindependent set of conflict graphs, converts the non-constrained binaryoptimization equation into Ising model of the quantum system, andcalculates the Hamiltonian of Ising model based on quantum dots toobtain solution of the non-constrained binary optimization equation.

For example, the quantum processing processor may comprise quantum dotsarranged in a matrix shape.

For example, neighboring quantum dots with the shortest distance in acolumn direction or a row direction are connected to each other throughthe tunnel junction.

For example, the quantum processing processor may further comprise acharge detection unit disposed adjacent to the quantum dots.

For example, the quantum processing processor may calculate theHamiltonian of the Ising model through adiabatic evolve.

As described above, according to the quantum dot-based quantummechanical machine vision system and an arithmetic operation method ofthe present invention, the NP problem generated as the number of featurepoints increases is replaced by Hamiltonian using Ising model, so thatit can be easily calculated using quantum dots arranged in a matrixshape.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings, which are included to provide a furtherunderstanding of the invention and are incorporated in and constitute apart of this specification, illustrate embodiments of the invention, andtogether with the description serve to explain the principles of theinvention.

FIG. 1 is a diagram showing a modeling of interrelationships of featurevectors between interest points according to an embodiment of thepresent invention.

FIG. 2 is a conceptual diagram showing two quantum dots spin qubit.

FIG. 3 is a conceptual diagram showing the arrangement of quantum dotsof a quantum processing processor according to an exemplary embodimentof the present invention.

FIG. 4 is a block diagram showing a quantum-dot-based quantum mechanicalmachine vision system in accordance with an exemplary embodiment of thepresent invention.

DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENTS

The present invention is described more fully hereinafter with referenceto the accompanying drawings, in which example embodiments of thepresent invention are shown. The present invention may, however, beembodied in many different forms and should not be construed as limitedto the example embodiments set forth herein. Rather, these exampleembodiments are provided so that this disclosure will be thorough andcomplete, and will fully convey the scope of the present invention tothose skilled in the art. In the drawings, the sizes and relative sizesof layers and regions may be exaggerated for clarity.

Hereinafter, exemplary embodiments of the present invention will bedescribed in detail with reference to the accompanying drawings.

FIG. 1 is a diagram showing a modeling of interrelationships of featurevectors between interest points according to an embodiment of thepresent invention.

In the machine vision system, the computer or the robot compares thepreviously captured reference pattern with the photographed image torecognize the image, and this process is advanced through a trainingprocess. In general, an algorithm called a heuristic algorithm isapplied to a particular type of image, and a heuristic algorithm can beapplied in various ways depending on the image.

Generally, a brain recognizing human visual and visual informationextracts feature points that can adequately describe a patternrepresented by each image for pattern matching between different images,and the distance and direction between the feature points aresynthetically recognized, so that the distance and direction arerecognized as a pattern. The human brain then compares the patterninformation extracted from the image to determine whether the two imagesmatch. This process is difficult by searching only by movement between apoint and a point, but easy by obtaining patterns including surroundingpoints.

However, in machine vision with limited intelligence in general, it isextremely difficult to fully simulate the behavior of human brain or theinterpretation of human sensory data. It is known as the NP-Hard Problemto simulate the behavior of the human brain.

In FIG. 1, a process of recognizing a pattern between different imagesis modeled, and the process is described as a general NP-Hard problem.The images of image A and image B are different images but may bedifferent versions of images having the same physical structure.

In order to perform pattern recognition operations related to machinevision, a combination of feature vectors representing relative positioninformation between respective points of interest (feature points) ineach image is used, and a combination of these feature vectors is usedas a reference for recognizing each image.

The process of extracting a reference pattern for each image can beperformed by a process of extracting feature points and a process ofdetermining relative position information between the feature points asa feature vector. This process is not a deterministic problem, but anon-deterministic problem in which it is necessary to find an optimizedvalue by comparing the results.

Assuming that a reference pattern made up of a set of feature vectorsbetween interest points (feature points) i, j, k in the image A in FIG.1 is X, and a reference pattern made up of a set of feature vectorsbetween interest points (feature points) α, β, γ in the image B in FIG.1 is Y, it is difficult to calculate the reference pattern X of image Aand the reference pattern Y of image B in FIG. 1.

In order to describe the mapping between the image A and the image B inFIG. 1, a reference pattern X which best describes image A and areference pattern Y which best describes image B must be obtained, andhow the reference pattern X is displaced to the reference pattern Y mustbe derived through calculation. That is, searching for a relationshipdescribing the mapping between the image A and the image B in FIG. 1 canbe regarded as searching for the most optimized combination of thereference pattern X and the reference pattern Y. In the presentinvention, this process is set as one objective function, and it isconsidered as an optimization problem in which the objective function isminimized. The optimization problem at this time is known as NP-hardproblem as mentioned above.

In the present invention, this optimization problem is solved by usingquantum computing, and an arrow representing a connection betweenrespective points of interest (feature points) is modeled as a dipole inan image. In this case, the arrow indicates the direction and lengthbetween the respective points of interest (feature points), and may berepresented by a vector.

To this end, (i) a term indicating a mismatch between a feature point ofthe image A and a corresponding position of the feature point of theimage B, and (ii) a term indicating spatial consistency betweenneighboring points can be defined by measuring divergence of matches ofthe neighboring points.

By utilizing the physical model of quantum computing, the most optimizedpattern X in image A and the most optimized pattern Y image B can befound at the same time. By modeling together with a combination offeature vectors between interest points (feature points) i, j, k in theimage A and a combination of feature vectors between interest points(feature points) α, β, γ in the image B as a physical model for quantumcomputing, and by observing the physical model, optimized referencepatterns X and Y can be obtained. The optimized state can be obtained bytaking the state of the physical model when the energy of the physicalmodel is in the ground state. For example, when a physical model isimplemented in a black box capable of quantum computing and physicalproperties of a physical model in a black box are observed when thetarget state (ground state) is obtained through an adiabatic evolutionprocess using a physical model, the optimized reference patterns X and Ycan be obtained.

At this time, the physical model including the dipole physicalcharacteristics such that the combination of vectors between interestpoints (feature points) of each image is described by the dipole modelcan be selected as the physical model in the black box.

In the image A in FIG. 1, a feature vector having the starting point ofinterest (feature point) i and the ending point of j can be expressed as{right arrow over (g_(i,j))}. In this case, the relationship between thepoints of interest (feature points) i to j includes not only thetranslation between the feature points but also the difference of thelocal scale and the orientation. Feature vectors {right arrow over(g_(i,j))} can be normalized for global translation, rotation, andscaling.

When the graph of the feature points i, j, k in image A of FIG. 1 isdefined as G_(A) and the graph of the points of interest (featurepoints) α, β, γ in image B is defined as G_(B), following Equation 1defines the distance between feature points (i∈G_(A), α∈G_(B)) derivedfrom each image. If the number of feature points in image A is M, theG_(A) is expressed as a labeled graph having M nodes. If the number offeature points in image B is N, the G_(B) is represented by a labeledgraph having N nodes. Where {right arrow over (f_(i))} is the normalizedfeature vector for the i^(th) vertex of the G_(A) and {right arrow over(f_(α))} is the normalized feature vector for the α^(th) vertex ofG_(B). The normalized feature vector may also be referred to as a localdescriptor depending on the document. For example, the normalizedfeature vector may be a vector based on Gabor wavelets of varying scaleand orientation with varying magnitude and direction around the point ofinterest. The edges of the graphs G_(A) and G_(B) represent thegeometric relationships between the feature vectors. Similarity betweenthe image A and the image B in FIG. 1 can be confirmed by finding thesimilarity between the two labeled graphs G_(A) and G_(B).

d(i,α)=d _(feature)({right arrow over (f)} _(i) ,{right arrow over (f)}_(α)),  [Equation 1]

where d (i, α) is a scalar product between feature vectors {right arrowover (f)}_(i) and {right arrow over (f)}_(α), and d (i, α) can beinterpreted as a measure of the similarity of the correlated featurevectors and is a normalized value.

At this time, the combination between the point i obtained in image Aand the point a obtained in image B can be defined as (i, α). If wedefine T_(feature) as a point-wise threshold that indicates whether thecombination (i, α) is a potential match suitable for describing thepattern, the combination (i, α) satisfying d (i, α)>T_(feature) can beinterpreted as a potential match suitable for describing the imagepattern.

The conflict graph G_(C) can be generated from the graphs G_(A) andG_(B) as a measure for measuring the similarity of the graphicalrepresentations of image A and image B in FIG. 1. The conflict graphG_(C) can be generated by sequentially adding possible point-to-pointcombinations suitable for describing the image pattern, starting fromthe combination (i, α) having the largest d (i, α) value as the vertexV_(iα) of the conflict graph G_(C). The process of generating a conflictgraph G_(C) can be repeated until all suitable point-to-pointcombinations are included.

Edges (i,α;j,β) in the conflict graph G_(C) encode geometric consistencybetween {right arrow over (f)}_(i) and {right arrow over (f)}_(j) in thelabelled graph G_(A) corresponding to image A in FIG. 1, and {rightarrow over (f)}_(α) and {right arrow over (f)}_(β) in the labelled graphG_(B) corresponding to image B in FIG. 1.

For all vertex pairs (V_(iα),V_(jβ)) in G_(C) where i≠j and α≠β wecalculate the geometric consistency of the two pairs of interest pointsd(i,α,j,β)=d_(geometric)({right arrow over (g)}_(i,j),{right arrow over(g)}_(αβ)) which is normalized.

The geometric consistency measures the geometric compatibility of thematch pairs (i,α) and (j,β) as the residual differences in localdisplacement, scale and rotation assignment of the associated interestpoints after the changes due to global translation, rotation and scalinghave been normalized. A pair (i,α) and (j,β) are not allowed to match ifthey are in geometric conflict, i.e., the residual effects are twolarge.

If d(i,α,j,β)<T_(geometric), the pair (i,α) and (j,β) are considered ingeometric conflict for a threshold T_(geometric). We draw an edge inG_(C) between vertex pairs (V_(iα),V_(jβ)) if i≠j and α≠β and they ingeometric conflict. By this prescription, we draw the conflict graphwith at most L vertices. The maximum independent set of the conflictgraph is equivalent to the maximum common subgraph of unlabeled graphsG_(A) and G_(B).

Finding the maximum independent set for the conflicting graph G_(C) canbe translated as a quadratic unconstrained binary optimization problemdefined by following Equation 2.

$\begin{matrix}{{{\overset{harpoonup}{x}}_{opt} = {\arg \mspace{11mu} \min \{ {\sum\limits_{{i\; \alpha} < {j\; \beta}}^{N}{Q_{{i\; \alpha},{j\; \beta}}x_{i\; \alpha}x_{j\; \beta}}} \}}},{x_{i\; \alpha} \in \{ {0,1} \}},} & \lbrack {{Equation}\mspace{14mu} 2} \rbrack\end{matrix}$

where Q_(iα,iα)=−1 for all vertices and Q_(iα,jβ)=L when there is anedge between the pair (i,α) and (j,β).

The minimum energy configuration enforces x_(iα)=1 if and only if V_(iα)belongs to the maximum independent set and x_(iα)=0 otherwise. Equation2 is a well know NP-hard problem which requires tremendous amount ofcomputation time as L grows.

In the following, Equation 2 is modified to apply to adiabatic quantumcomputation for a quantum Ising Model.

Let X (where

$ {X = \begin{pmatrix}x_{1} \\x_{2} \\x_{3} \\\vdots \\x_{N}\end{pmatrix}} )$

be a column vector of N Boolean variables and Q is a N×N matrix suchthat, then Equation 2 can be rewritten as the following Equation 3.

X _(opt)=argmin X ^(†) QX wherein x _(i)∈(0,1}.  [Equation 3]

On the other hand, quantum mechanical Ising problem is formulated as thefollowing Equation 4 by applying the relation of S=2X−1 to the Equation3.

S _(opt)=argmin{S ^(†) JS+h ^(†) S} where S _(i)∈{−1,1}.  [Equation 4]

The S variables are called quantum-mechanical spin. This quantum Isingmodel can be solved by one particular model of quantum computationcalled adiabatic quantum computation (AQC).

In quantum mechanics, the spin states S=±1 are represented by orthogonalvectors in Hilbert space denoted as qubits. The two state of qubits aredescribed by vectors as the following Equation 5.

$\begin{matrix}{{0\rangle} = {{\begin{pmatrix}1 \\0\end{pmatrix}\mspace{14mu} {and}\mspace{14mu} {1\rangle}} = {\begin{pmatrix}0 \\1\end{pmatrix}.}}} & \lbrack {{Equation}\mspace{14mu} 5} \rbrack\end{matrix}$

The qubits can be extended to a vector by a linear combination calledsuperposition, and this process is expressed as Equation 6.

|ϕ

=α|0

+β|1

with |α|²+|β|²=1.  [Equation 6]

Larger quantum systems are constructed through tensor product of theindividual qubit vector spaces, for example, as the following Equation7.

$\begin{matrix}{{01\rangle} = {{{0\rangle} \otimes {1\rangle}} = {\begin{pmatrix}0 \\1 \\0 \\0\end{pmatrix}.}}} & \lbrack {{Equation}\mspace{14mu} 7} \rbrack\end{matrix}$

Superpositions of N qubit states are also possible with the associatedamplitudes representing the probability of observing the respective Nspin state.

We also define single qubit operators can be defined as the followingEquation 8.

$\begin{matrix}{I = {{\begin{pmatrix}1 & 0 \\0 & 1\end{pmatrix}\mspace{14mu} {and}\mspace{14mu} \sigma^{z}} = {\begin{pmatrix}1 & 0 \\0 & {- 1}\end{pmatrix}.}}} & \lbrack {{Equation}\mspace{14mu} 8} \rbrack\end{matrix}$

If the operator of Equation (8) is applied to the qubit vector ofEquation (5), the following Equation (9) can be obtained.

σ²|0

=|0

,σ^(x)|1

=−|1

.  [Equation 9]

On 2-qubit state, an operator σ^(z)⊗I extracts the classical spin of thefirst qubit, I⊗σ^(z) extracts the classical spin of the second qubit andσ^(z)⊗σ^(z) extracts the product of the two classical spins.

The quantum-mechanical Ising model on N spins is represented as2^(N)×2^(N) Hamiltonian represented as the following Equation 10.

$\begin{matrix}{{H_{I} = {{\sum\limits_{i,j}{J_{ij}\sigma_{i}^{z}\sigma_{j}^{z}}} + {\sum\limits_{i}{h_{i}\sigma_{i}^{z}}}}},} & \lbrack {{Equation}\mspace{14mu} 10} \rbrack\end{matrix}$

where σ_(i) ^(z) is an operator σ^(z) acting on i^(th) qubit.

To initialize the quantum system, another kind of spin operator σ^(x)can be defined as shown in Equation 11.

$\begin{matrix}{\sigma^{x} = \begin{pmatrix}0 & 1 \\1 & 0\end{pmatrix}} & \lbrack {{Equation}\mspace{14mu} 11} \rbrack\end{matrix}$

The spin operator of Equation 11 can flip the state of the qubit.

At this time, the ground state Hamiltonian can be expressed by followingEquation 12 using a spin operator acting on the i^(th) qubit.

$\begin{matrix}{H_{0} = {\Delta {\sum\limits_{i}{\sigma_{i}^{x}.}}}} & \lbrack {{Equation}\mspace{14mu} 12} \rbrack\end{matrix}$

The eigenstate of the ground state Hamiltonian of Equation 12 can beexpressed as following Equation 13.

$\begin{matrix}{{\Phi\rangle}_{0} = {\otimes_{i}{( \frac{{0\rangle}_{i} - {1\rangle}_{i}}{\sqrt{2}} ).}}} & \lbrack {{Equation}\mspace{14mu} 13} \rbrack\end{matrix}$

The time dependency of the quantum state of Equation 13 can be expressedby the Schrödinger equation of Equation 14.

$\begin{matrix}{{i\; \hslash \frac{\partial}{\partial t}{{\Psi (t)}\rangle}} = {{H(t)}{{{\Psi (t)}\rangle}.}}} & \lbrack {{Equation}\mspace{14mu} 14} \rbrack\end{matrix}$

To solve the quantum mechanical eigen modeling adiabatically, the convexform of the adiabatic Hamiltonian is obtained by using the initialcondition given by |Ψ(0)>=|Ψ>0 at t=0.

$\begin{matrix}{{H(t)} = {{( {1 - \frac{t}{T}} )H_{0}} + {\frac{t}{T}H_{I}}}} & \lbrack {{Equation}\mspace{14mu} 15} \rbrack\end{matrix}$

At t=0, the quantum system has the lowest energy state. At this time,the lowest energy state can give equal probability for all classicalconfigurations. On the other hand, at t=T, it is designed to cope withthe quantum mechanical Ising model problem to solve the artificialvisual problem.

In this way, the NP-hard problem, which is difficult to classicallyhandle, can be solved through quantum mechanical adiabatic evolution ofa given quantum system.

The globally lowest classical configuration obtained by adiabaticquantum mechanics (AQC) can be a solution to the second-order,non-definite binary optimization problem, which is a complexcomputational problem related to artificial view. It has beenmathematically proved that quantum computing can provide exponentialspeed-up in solving NP-hard problems compared to classical methods.

The process of training the adiabatic quantum computing system to solvethe secondary unrestricted binary optimization problem defined byEquation 2 begins with hardware training using a classificationalgorithm. The classification algorithm is expressed by the followingequation 16.

$\begin{matrix}{{y = {{sign}( {\sum\limits_{i = 1}^{N}{\omega_{i}{h_{i}(x)}}} )}},} & \lbrack {{Equation}\mspace{14mu} 16} \rbrack\end{matrix}$

where x∈R^(M) are input patters to be classified, y∈{−1,1} is the outputof the classifier, h_(i):R^(M)→{−1,1} are feature detectors, andω_(i)∈{0,1} is the weights to be optimized during training.

The training is achieved by solving the discrete optimization problemexpressed as the following Equation 17.

                                     [Equation  17]${\underset{\_}{\omega}}_{opt} = {{\underset{\omega}{argmin}( \underset{\_}{{{{\underset{\_}{\omega}}^{\dagger}( {\frac{1}{N^{2}}{\sum\limits_{s = 1}^{S}{{\underset{\_}{h}( {\underset{\_}{x}}_{s} )}{\underset{\_}{h}( {\underset{\_}{x}}_{s} )}^{\dagger}}}} )}\underset{\_}{\omega}} + {\underset{\_}{\omega}( {{\lambda \; I} - {2{\sum\limits_{s = 1}^{S}{\frac{\underset{\_}{h}( {\underset{\_}{x}}_{s} )}{N}y_{s}}}}} )}} )}.}$

Here, the above Equation 17 is described for S-number of trainingsamples {(x_(s) ,y_(s))|=1, 2, . . . , S}.

Hereinafter, a hardware implementation for solving the machine visionproblem and a mathematical expression for describing the hardware willbe described.

FIG. 2 is a conceptual diagram showing two quantum dots spin qubit.

FIG. 2 shows the electrons confined in quantum dots 121 with spin

${\overset{harpoonup}{S}}_{1,2} = {\frac{1}{2}{\hslash\sigma}_{1,2}^{z}}$

connected via tunnel junction 122. Those quantum dots 121 can befabricated via gate-defined quantum dot structure. The Hamiltonian forthis system is given by the following Equation 18.

H=J ₁₂(t)σ₁ ^(z)σ₂ ^(z) +h ₁σ₁ ^(z) +h ₂σ₂ ^(z)  [Equation 18]

In this equation, J₁₂ (t) is controlled by an external bias. Theindividual spin detection of the electrons is performed by the chargedetection unit 123.

On the other hand, Hamiltonian regarding to N quantum dots can bedescribed by the following equation 19.

$\begin{matrix}{H_{I} = {{\sum\limits_{i < j}{J_{ij}\sigma_{i}^{z}\sigma_{j}^{z}}} + {\sum\limits_{i}{h_{i}\sigma_{i}^{z}}}}} & \lbrack {{Equation}\mspace{14mu} 19} \rbrack\end{matrix}$

In Equation 19, J_(ij) and h_(i) are variables having a positive value,and are changed as the external power source is applied. The biasvoltage applied to the gate can be appropriately adjusted to calculatethe Hamiltonian of the quantum processing processor.

Hamiltonian at the initial (t=0) is J_(ij)=0 for all i and j. InEquation 15, the T value is defined as T=ℏ/ΔE, and ΔE is the intervalbetween the initial ground state and the global minimum energy.

FIG. 3 is a conceptual diagram showing the arrangement of quantum dotsof a quantum processing processor according to an exemplary embodimentof the present invention, and FIG. 4 is a block diagram showing aquantum-dot-based quantum mechanical machine vision system in accordancewith an exemplary embodiment of the present invention.

Referring to FIG. 3 and FIG. 4, a quantum dot based quantum mechanicalmachine vision system 100 according to an exemplary embodiment of thepresent invention may include an image acquisition module 110, a quantumprocessing processor 120 and a memory unit 130.

The image acquisition module 110 acquires an image. The imageacquisition module 110 may include, for example, a CCD camera.

The quantum processing processor 120 processes the image obtained fromthe image acquisition module 110.

The memory unit 130 stores data necessary for the computation of thequantum processing processor 120.

The quantum processing processor 120 obtains a first labeled graphconnecting between feature points of the first image and a secondlabeled graph connecting feature points of the second image, generates apoint-to-point combination by matching the feature points of the firstimage with the feature points the second image, generates a conflictgraph by adding the largest point-to-point combination by comparing thepoint-to-point combinations with the threshold, generatesnon-constrained binary optimization equation for finding a maximumindependent set of conflict graphs, converts the non-constrained binaryoptimization equation into Ising model of the quantum system, andcalculates the Hamiltonian of Ising model based on the quantum dots toobtain solution of the non-constrained binary optimization equation. Thequantum processing processor 120 may learn repeatedly thenon-constrained binary optimization equation through machine learning.

For example, the quantum processing processor 120 may include quantumdots 121 arranged in a matrix shape as shown in FIG. 3.

At this time, neighboring quantum dots 121 with the shortest distance ina column direction or a row direction may be connected to each otherthrough the tunnel junction 122.

The quantum processing processor 120 may further include a chargedetection unit 123 disposed adjacent to the quantum dot 121 fordetecting electrons of the quantum dot 121.

Meanwhile, in calculating the Hamiltonian of Ising model based on thequantum dots 121 to obtain solution of the non-constrained binaryoptimization equation, the Hamiltonian of Ising model can be calculatedthrough adiabatic evolve. This process has been described in detailabove, so redundant description is omitted.

As described above, according to the quantum dot-based quantummechanical machine vision system and an arithmetic operation method ofthe present invention, the NP problem generated as the number of featurepoints increases is replaced by Hamiltonian using Ising model, so thatit can be easily calculated using quantum dots arranged in a matrixshape.

It will be apparent to those skilled in the art that variousmodifications and variation may be made in the present invention withoutdeparting from the spirit or scope of the invention. Thus, it isintended that the present invention cover the modifications andvariations of this invention provided they come within the scope of theappended claims and their equivalents.

What is claimed is:
 1. A quantum mechanical arithmetic operation methodbased on quantum dots, the quantum mechanical arithmetic operationmethod being performed by a quantum processing processor, the quantummechanical arithmetic operation method comprising: obtaining a firstlabeled graph connecting between feature points of the first image and asecond labeled graph connecting feature points of the second image;generating a point-to-point combination by matching the feature pointsof the first image with the feature points the second image; generatinga conflict graph by adding the largest point-to-point combination bycomparing the point-to-point combinations with the threshold; generatingnon-constrained binary optimization equation for finding a maximumindependent set of conflict graphs; converting the non-constrainedbinary optimization equation into Ising model of the quantum system; andcalculating the Hamiltonian of Ising model based on the quantum dots toobtain solution of the non-constrained binary optimization equation. 2.The quantum mechanical arithmetic operation method of claim 1, whereincalculating the Hamiltonian of Ising model based on the quantum dots toobtain solution of the non-constrained binary optimization equation isperformed by quantum dots arranged in a matrix shape.
 3. The quantummechanical arithmetic operation method of claim 2, wherein neighboringquantum dots with the shortest distance in a column direction or a rowdirection are connected to each other through the tunnel junction. 4.The quantum mechanical arithmetic operation method of claim 1, whereinthe Hamiltonian of the Ising model is calculated through adiabaticevolve, in calculating the Hamiltonian of Ising model based on thequantum dots to obtain solution of the non-constrained binaryoptimization equation.
 5. The quantum mechanical arithmetic operationmethod of claim 1, further comprising: repeatedly learning thenon-constrained binary optimization equation through machine learning.6. A quantum mechanical machine vision system comprising: an imageacquisition module configured to acquire an image; a quantum processingprocessor configured to process the image obtained from the imageacquisition module; and a memory unit configured to store data necessaryfor computation of the quantum processing processor; wherein the quantumprocessing processor, obtains a first labeled graph connecting betweenfeature points of the first image and a second labeled graph connectingfeature points of the second image, generates a point-to-pointcombination by matching the feature points of the first image with thefeature points the second image, generates a conflict graph by addingthe largest point-to-point combination by comparing the point-to-pointcombinations with the threshold, generates non-constrained binaryoptimization equation for finding a maximum independent set of conflictgraphs, converts the non-constrained binary optimization equation intoIsing model of the quantum system, and calculates the Hamiltonian ofIsing model based on quantum dots to obtain solution of thenon-constrained binary optimization equation.
 7. The quantum mechanicalmachine vision system of claim 6, wherein the quantum processingprocessor comprises quantum dots arranged in a matrix shape.
 8. Thequantum mechanical machine vision system of claim 7, wherein neighboringquantum dots with the shortest distance in a column direction or a rowdirection are connected to each other through the tunnel junction. 9.The quantum mechanical machine vision system of claim 7, wherein thequantum processing processor further comprises a charge detection unitdisposed adjacent to the quantum dots.
 10. The quantum mechanicalmachine vision system of claim 6, wherein the quantum processingprocessor calculates the Hamiltonian of the Ising model throughadiabatic evolve.